(See attached file for full problem description with proper symbols and equations)
---
First: solve this problem.
Second: check my answer.
Third: if my answer is wrong or incomplete explain why.
Explain why cannot have more than one root.
This is how I tried to solve it:
I used the interval [-1,1]
By

A) Show that if b<a the conformal transformation....maps a circle of radius 'a' in the plane into an ellipse in the ...plane.
b) Show that the velocity on the surface of an ellipse in a uniform horizontal flow of velocity U reaches a maximum when theta = 90 degrees and has a magnitude of...
c) Determine the velocity on the sur

A=1,B=2,C=3,D=4,E=5,........X=24,Y=25,Z=26
It is enciphered using the rule
35
R (m)=m (mod 91)
35
The resulting ciphertext is ( 73,14,23,73,23)
Verify the rule given satisfy the condition for an RSA cipher.
Using the repeated squaring technique decipher the ciphertext and find the message

Prove that if p is a polynomial with real coefficients, and if is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions.
Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the "shift operator" for a sequence.

1). Determine the set A such that
For r > 0 let A ={w, w = exp (1/z) where 0<|z|<r}.
2).Prove that there is no branch of the logarithm defined on G= C-{0}.
( C here is the complex plane).
( Hint: suppose such a branch exists and compare this with the principal branch).
I want detailed proofs and please prove ever

Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imaginary axes.
The 2 theorems are:
1). Theorem: Suppose f: X --> omega is continuou

A payoff table is given as
.....
a. What choice should be made by the optimistic decision maker?
b. What choice should be made by the conservative decision maker?
c. What decision should be made under minimax regret?
d. If the probabilities of E, F, and G are .2, .5, and .3, respectively, then
e. What choice should be ma

4. (Separation) Seeking a solution u(x, t) = X(x)T(t) for the given PDE, carry out steps analogous to equations (3)?(6), and derive ODE's analogous to (7a,b). Take the separation constant to be ?K2, as we do in (6). Obtain general solutions of those ODE's (distinguishing any special ic values, as necessary) and use superposition

A. A certain fluid is flowing with a constant speed V in a direction making an angle B with the positive x-axis. Find the complex potential for the fluid under consideration.
Also determine the velocity and the stream functions.